Asynchronous or async means a thing that is not synchronized. In easy way asynchronous is method of transferring data intermittently rather than one by one transmission. This term is basically used in technology for communication and data transfer methods.
Illustration: A telephone conversation is always asynchronous; because at the both end we can talk any time when we want and both the parties can listen each of them easily without any issue. If telephone conversation was synchronous, then it would be difficult to talk because at the both end, each of them have to wait for front person to complete its talk and we need to reply after him.
The biggest problem with asynchronous communication and data transmission is that the receiver should have a method of distinguishing the valid data. Like in computer communication we use start bit or stop bit to define the valid data and it is attached with at the each ends of the data.
In web development, asynchronous method is used to loading files like JavaScript and AJAX files quickly as soon as possible with loading all of them on one time frame rather than loading them one by one.